A class ofA-stable two-step methods based on Schur polynomials

Abstract

Lineark-step methods (k≧2) with constant coefficients are derived by choosing as the second characteristic polynomial of the method a Schur polynomial whose coefficients depend on a certain set of parameters. The choice of these parameters is based on a result due to Marden concerning the location of the zeros of a class of rational functions, and it is shown that, for the (practically important) casek=2, the corresponding two-step methods are alwaysA-stable.